Related papers: Canonical Wick rotations in 3-dimensional gravity
In this article we first develop novel Rindler-type representations of flat spacetime by demonstrating that the standard hyperbolic transformation is a member of an infinite family of coordinate mappings. We specifically introduce cyclic…
In a recent work we presented a reformulation of the canonical quantum gravity, based on adding the so-called kinematical term to the gravity-matter action; this revised approach leads to a self-consistent canonical quantization of the…
The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to the (non-compact) hyperbolic space. We prove the globally nonlinear stability of the open Milne spacetime for both massive and massless Einstein-scalar…
A lattice quantum gravity model in 4 dimensional Riemannian spacetime is constructed based on the SU(2) Ashtekar formulation of general relativity. This model can be understood as one of the family of models sometimes called ``spin foam…
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
We study the mean curvature flow of smooth $m$-dimensional compact submanifolds with quadratic pinching in the Riemannian manifold $\mathbb{C}P^n$. Our main focus is on the case of high codimension, $k\geq 2$. We establish a codimension…
All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is…
We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a ``canonical initial slope" for…
Spacelike surfaces in Generalized Robertson-Walker spacetimes whose mean curvature function satisfies a natural nonlinear inequality are analyzed. Several uniqueness and nonexistence results for such compact spacelike surfaces are proved.…
In this paper, we first give some new characterizations of geodesic spheres in the hyperbolic space by the condition that hypersurface has constant weighted shifted mean curvatures, or constant weighted shifted mean curvature ratio, which…
We study rotational surfaces with constant Minkowski Gaussian curvature and rotational surfaces with constant Minkowski mean curvature in a $3$-dimensional normed space with rotationally symmetric norm. We have a generalization of the…
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
We affirmatively solve the analogue of Lord Rayleigh's conjecture on Riemannian manifolds with positive Ricci curvature for any clamped plates in 2 and 3 dimensions, and for sufficiently large clamped plates in dimensions beyond 3. These…
We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean…
We characterise the (fake) supersymmetric solutions of Wick-rotated N=2 d=4 gauged supergravity coupled to non-Abelian vector multiplets. In the time-like case we obtain generalisations of Kastor & Traschen's cosmological black holes: they…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version…
In the context of canonical quantum gravity, we study an alternative real quantisation scheme, which is arising by relating simpler Riemannian quantum theory to the more complicated physical Lorentzian theory - the generalised Wick…